JP2005318631A - Method for reducing peak-to-average power ratio using code book in code division multiple access communication, and apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a CDMA system whose peak-to-average power ratio is reduced. <P>SOLUTION: The invention is a method and apparatus for generating a code book used in the CDMA system. The code book is composed of a plurality of vectors used for coding a user data. An amplitude and a polarity of each vector of the code book are selected, to reduce the peak-to-average power ratio. Amplitude value can be selected, to reduce the peak-to-average power ratio, while maintaining a desired average energy per chip. The desired energy per chip can be based on energy per chip in the CDMA system, having a lower-order spreading factor. Furthermore, performance can be improved, by using a first code book under the condition of a first signal-to-noise ratio, and by using a second code book under the condition of a second signal-to-noise ratio. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a CDMA (Code Division Multiple Access) communication system, and more particularly, to a DS-CDMA (Direct Sequence CDMA) system that reduces PAPR (Peak to Average Power Ratio).

  In the CDMA technology, a plurality of information signals are transmitted on the same channel, and each user subchannel is encoded with a unique spreading code to be differentiated. Initially, CDMA networks were designed to carry only voice traffic, so the variability in data rate was limited. Now, however, CDMA networks are evolving to encompass a variety of applications, each requiring potentially different data rates and quality of service. A CDMA system using four spreading codes has a “spreading factor” of four and can transmit four separate data streams.

The output of a given CDMA transmitter is generally the sum s of each data stream multiplied by its corresponding spreading code. For a system with a spreading factor of 4, there can be 16 output vectors s . It will be apparent that such CDMA peak-to-average power ratio is the maximum across all possible output vectors s , although peak energy divided by average energy. Obviously, when the peak-to-average power ratio in a CDMA system is greater than 1, the power of the various signals varies. Thus, as is often seen in communication devices, when the output vector s is amplified with a non-linear amplifier before transmission, the transmitted signal is amplified differently for each possible output vector s , thereby Non-linear distortion occurs.
T.A. Ottosson “Precoding for Minimization of Envelope Variations in Multicode DS-CDMA Systems”, Wireless Personal Communications, 13, 57-78, 2000 F. J. et al. MacWilliams, N.M. J. et al. A. Sloane, “The Theory of Error-Correcting Codes”, North-Holland, 1977 F. J. et al. MacWilliams, N.M. J. et al. A. Slone, "The Theory of Error-Correcting Codes", Chapter 14.3, Series 3 L. R. Bahl et al., “Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate”, IEEE Trans. Inform. Theory, 20, pp. 284-87, 1974

  Therefore, a CDMA system that can reduce the peak-to-average power ratio is needed.

  Mainly, a method and apparatus for generating a code book for use in a CDMA system is provided. A code book consists of a plurality of vectors used to encode user data. According to one aspect of the invention, the amplitude and polarity of each vector in the code book is selected to reduce the peak to average power ratio. This amplitude value can be selected to reduce the peak to average power ratio while maintaining the desired average energy per chip. The desired energy per chip can be based on the energy per chip of a CDMA system having a lower order diffusion coefficient.

  In one exemplary implementation, a CDMA system has a spreading factor of 8 to convey eight separate data streams. One or more data streams can be reserved to maintain a desired data rate (eg, a CDMA system with a spreading factor of 4). The vectors used in the exemplary code book have amplitude values that can significantly reduce the peak-to-average power ratio as compared to the commonly used conventional CDMA system with a spreading factor of 4. In a further variation, the performance is further improved by using a first code book under conditions of a first signal to noise ratio and using a second code book under conditions of a second signal to noise ratio. Can be improved.

From a system point of view, a CDMA transmitter incorporating the features of the present invention comprises a plurality of multipliers that multiply the encoded data stream by a corresponding spreading code. The encoded data stream is based on a code book consisting of a plurality of vectors, each of which has non-uniform amplitude values selected to reduce the peak-to-average power ratio in accordance with the present invention. .
The invention and further features and advantages of the invention can be more fully understood with reference to the following detailed description and drawings.

  FIG. 1 shows a conventional DS-CDMA system 100 with a spreading factor (SF) of four. The conventional DS-CDMA system 100 is used in, for example, a mobile phone. Details of an exemplary DS-CDMA system 100 can be found, for example, in T.W. See Ottosson, “Precoding for Minimization of Envelope Variations in Multicode DS-CDMA Systems”, Wireless Personal Communications, 13, 57-78, 2000.

The conventional DS-CDMA system 100 shown in FIG. 1 is used to simultaneously transmit four information streams a ₀ , a ₁ , a ₂ , and a ₃ that carry information of streams ₀ , ₁ , ₂ , and ₃ , respectively. It is done. The variables a ₀ , a ₁ , a ₂ , a _{3 form} the vector a = (a ₀ , a ₁ , a ₂ , a ₃ ). The vector s is called an output vector and is output to the communication channel. The vectors c ₀ , c ₁ , c ₂ , c ₃ are spreading sequences. In general, each information stream a ₀ , a ₁ , a ₂ , a ₃ is multiplied by a corresponding spreading sequence c ₀ , c ₁ , c ₂ , c ₃ by a corresponding multiplier 110-1 to 110-4, respectively. These spread signals are combined at stage 120 and output to the channel.

したがって、これらのシーケンスは直交する。すなわち、

が成り立つ。ここで、乗算・は、次のルールで定義される、２つのベクトルの内積である。
（ｘ_０，ｘ_１，．．．，ｘ_ｎ−１）・（ｙ_０，ｙ_１，．．．，ｙ_ｎ−１）＝ｘ_０ｙ_０＋ｘ_１ｙ_１＋．．．ｘ_ｎ−１ｙ_ｎ−１
たとえば、
ｃ _１・ｃ _２＝（１，−１，１，−１）・（１，１，−１，−１）＝１−１−１＋１＝０であるが、
ｃ _１・ｃ _１＝（１，−１，１，−１）・（１，−１，１，−１）＝１＋１＋１＋１＝４である。 FIG. 2 shows an exemplary code book A 200 that can be used in the DS-CDMA system 100 of FIG. The vector a thus forms the code book A of FIG. The information bits of the i-th information stream are encoded into the code of the i-th entry of the vector a. Logic 0 (0) corresponds to the positive entry of vector a , and logic 1 (1) corresponds to the negative entry. For example, if a logic 0 is transmitted in the 0th and 3rd information streams, and a logic 1 is transmitted in the 1st and 2nd information streams, the vector a = (a, -a, -a, a) is transmitted. To do. The value a is the amplitude of the transmission signal. In general, the amplitudes of the four information streams a ₀ , a ₁ , a ₂ , a ₃ are the same. In some implementations of the conventional DS-CDMA system 100, the amplitude of one or more of the four information streams a ₀ , a ₁ , a ₂ , a ₃ is increased, correspondingly, Energy can be increased (and thus protection can be enhanced). For example, the amplitude of stream a ₀ that may be associated with the pilot signal can be increased to improve channel estimation.
The vectors c ₀ , c ₁ , c ₂ , c ₃ are spreading sequences assigned to the corresponding information streams.
The spreading sequences c ₀ , c ₁ , c ₂ , c ₃ are defined as follows:
c ₀ = (1,1,1,1)
c ₁ = (1, -1,1, -1)
c ₂ = (1,1, -1, -1)
c ₃ = (1, −1, −1,1)
These sequences form the rows of the well-known four-dimensional Hadamard matrix H ₄ as shown in the following equation (for example, FJ MacWilliams, NJA ASlone, “The Theory of Error− Collecting Codes ", North-Holland, 1977).

Therefore, these sequences are orthogonal. That is,

Holds. Here, multiplication is an inner product of two vectors defined by the following rule.
(X ₀ , x ₁ ,..., X _n−1 ) · (y ₀ , y ₁ ,..., Y _n−1 ) = x ₀ y ₀ + x ₁ y ₁ +. . . x _n-1 y _n-1
For example,
c ₁ · c ₂ = (1, -1,1, -1) · (1,1, -1, -1) = 1-1-1 + 1 = 0,
c ₁ · c ₁ = (1, -1,1, -1) · (1, -1,1, -1) = 1 + 1 + 1 + 1 = 4.

The output vector s = (s ₀ , s ₁ , s ₂ , s ₃ ) is transmitted to the channel after being modulated, and this vector is calculated by the following equation.
s = a · H ₄ = a ₀ c ₀ + a ₁ c ₁ + a ₂ c ₂ + a ₃ c ₃
The multiplication a _i c _i occupies time for 4 chips. Accordingly, a DS-CDMA system with a spreading factor of 4, such as the DS-CDMA system 100 of FIG. 1, changes the values of the variables a ₀ , a ₁ , a ₂ , a ₃ earlier than every four consecutive chips. I can't.

Therefore, the DS-CDMA system 100 is a system in which the variables a ₀ , a ₁ , a ₂ , and a ₃ take new values every 4 chips, and the variable a ₀ takes a new value only every m chips (m Is an integer divisible by 8. In the system 100, the 0th stream is to play a special role. For example, the 0th stream of the mobile phone can be used for audio transmission, and the other streams can be used for data transmission. Voice, since the change in comparison with the data is much slower, a ₀ may be taken a new value for each i chip consecutive. Another common and important case is when the 0th stream is used for pilot signal transmission. Usually, the pilot signal is constant over a long time interval (usually 256 chips), thus allowing the decoder to accurately estimate the channel fading coefficients.

復号化
ベクトルｓは、例示的なチャネルを介しての送信中に、付加雑音によって破損し、ベクトルｘ＝ｓ＋ｚが受信される（ｚは雑音のベクトルである）。ａ_ｉの値を復元するために、次式のように、受信ベクトルｘにベクトルｃ _ｉを乗ずる逆拡散手続きを用いる。
ｈ_ｉ＝ｘ・ｃ _ｉ＝（ｓ＋ｚ）・ｃ _ｉ＝（ａ_０ ｃ _０＋ａ_１ ｃ _１＋ａ_２ ｃ _２＋ａ_３ ｃ _３）・ｃ _ｉ＋ｚｃ _ｉ （３）
式（１）の直交性を考慮すると、次式が得られる。
ｈ_ｉ＝４ａ_ｉ＋ｚ・ｃ _ｉ
最後に、ｈ_ｉの符号を計算し、元のビットを

として再構成する。チャネル雑音があまり強くない場合、つまり、ベクトルｚのエントリが小さい数の場合は、高い確率で、量｜ｚ・ｃ_ｉ｜が｜４ａ_ｉ｜より小さくなる。したがって、ｈ_ｉはａ_ｉと同じ符号になり、

はａ_ｉと等しくなる。 The speed of the DS-CDMA system 100 is defined as the average number of information bits transmitted per chip. The speed of the DS-CDMA system 100 can be expressed as:

Decoding vector s is corrupted by additive noise during transmission over the exemplary channel, and vector x = s + z is received ( z is a vector of noise). In order to restore the value of a _i , a despreading procedure is used in which the received vector x is multiplied by the vector c _i as shown in the following equation.
_{h i = x · c i =} (s + z) · c i = (a 0 c 0 + a 1 c 1 + a 2 c 2 + a 3 c 3) · c i + zc i (3)
Considering the orthogonality of equation (1), the following equation is obtained.
h _i = 4a _i + z · c _i
Finally, to calculate the sign of h _i, the original bit

Reconfigure as. If the channel noise is not very strong, that is, if the number of entries in the vector z is small, the quantity | z · c _i | is less than | 4a _i | with high probability. Therefore, h _i has the same sign as a _i ,

Is equal to a _i .

が得られる。 For example, it can be assumed that a = 1 without loss of generality. If a = (1, -1,1,1) and z = (2.1, −1.8, −1.85, −1.75), then s = (2,2, −2,2) ) And h = (2.1, -1.8, -1.85, -1.75). For example, if h ₁ is calculated according to equation (3), h ₁ becomes −3.3,

Is obtained.

を再構成する。以下で定義する符号化エラーの確率が、ａ_０に関しては、他のａ_ｉの値の場合より格段に低くなることは明らかであろう。
ＤＳ−ＣＤＭＡシステム１００のようなＤＳ−ＣＤＭＡシステムのビット・エラー確率は、次のように定義される。

ＤＳ−ＣＤＭＡシステム１００のＰＡＰＲ
信号ｘ＝（ｘ_０，ｘ_１，．．．．，ｘ_ｎ−１）のエネルギーは、

で定義される。
したがって、出力ベクトルｓのチップ当たりの平均エネルギーは、次式のとおりである。

The variable a ₀ changes only for every m chips and is spread with the support of the sequence c ₀ = (1,1,1,1), so another rule is used to reconstruct the value of a ₀ . x ⁽ⁱ⁾ , i = 1,. . . , M / 4 represents a vector received from the channel after transmitting m chips. z ⁽ⁱ⁾ , i = 1,. . . , M / 4 represents the corresponding noise vector. To find the value a ₀ , calculate

Reconfigure. It will be apparent that the coding error probability defined below is much lower for a ₀ than for other values of a _i .
The bit error probability of a DS-CDMA system, such as DS-CDMA system 100, is defined as follows:

PAPR of DS-CDMA system 100
The energy of the signal x = (x ₀ , x ₁ ,..., X _n−1 ) is

Defined by
Therefore, the average energy per chip of the output vector s is as follows:

ｓのピーク・エネルギーは次式で定義される。

ＤＳ−ＣＤＭＡシステム１００のピーク対平均電力比は次のとおりである。

したがって、ピーク対平均電力比は変動する。携帯電話などの通信装置においてよく見られる非線形増幅器の場合、送信信号の各成分がそれぞれ異なるように増幅され、それによって、非線形歪みが発生する。そこで、ピーク対平均電力比を低減できるＤＳ−ＣＤＭＡシステムが必要とされる。
Ｈ_ｎをｎ次元のアダマール行列とし、ｙ＝（ｙ_０，．．．，ｙ_ｎ−１）を実ベクトルとし、ν＝ｙＨ_ｎとする。パーセバルの公式（たとえば、Ｆ．Ｊ．ＭａｃＷｉｌｌｉａｍｓ、Ｎ．Ｊ．Ａ．Ｓｌｏａｎｅ、「Ｔｈｅ Ｔｈｅｏｒｙ ｏｆ Ｅｒｒｏｒ−Ｃｏｒｒｅｃｔｉｎｇ Ｃｏｄｅｓ」、第１４．３章、系３を参照されたい）によれば、次式で表されるベクトルｙのエネルギーは、

次の等式によって、ベクトルνのエネルギー

に関係付けられる。
Ｅ（ν）＝ｎＥ（ｙ） （７）
ベクトルａ＝（ａ_０，ａ_１，ａ_２，ａ_３）が送信されると、パーセバルの公式（式（７））に従って、対応する出力ベクトルｓは、次式で与えられるチップ当たりの平均エネルギーを有する。

したがって、式（４）から次式が成り立つ。
Ｅ_Ａ＝４ａ^２ （９） The average energy per chip of this system is the value E ( s ), which is the average of all 16 possible vectors s corresponding to the vectors in code book A shown in FIG. Defined.

The peak energy of s is defined by the following equation.

The peak-to-average power ratio of the DS-CDMA system 100 is as follows.

Thus, the peak to average power ratio varies. In the case of a nonlinear amplifier often found in a communication device such as a cellular phone, each component of the transmission signal is amplified differently, thereby generating nonlinear distortion. Therefore, there is a need for a DS-CDMA system that can reduce the peak-to-average power ratio.
_Let H _n be an n-dimensional Hadamard matrix, y = (y ₀ ,..., Y _n-1 ) be a real vector, and ν = y H _n . According to Perseval's formula (see, for example, F.J.MacWilliams, N.J.A. Sloane, "The Theory of Error-Correcting Codes", Chapter 14.3, System 3), The energy of the vector y represented is

The energy of the vector ν by the equation

Related to.
E ( ν ) = nE ( y ) (7)
When the vector a = (a ₀ , a ₁ , a ₂ , a ₃ ) is transmitted, according to the Parseval formula (equation (7)), the corresponding output vector s is the average energy per chip given by Have

Therefore, the following equation is established from the equation (4).
E _A = 4a ² (9)

Thereby, the PAPR of the DS-CDMA system 100 is estimated. Half of the output vector s = (s ₀ , s ₁ , s ₂ , s ₃ ) is 0 for three variables of s ₀ , s ₁ , s ₂ , s ₃ and the absolute value of one variable is | It will be clear that it has the property of 4a ² |. For example, if a = (a, a, −a, −a), the corresponding output vector has the form s = (0, 0, 4a, 0). The next half of the output vector has the property that all absolute values of the variables s ₀ , s ₁ , s ₂ , s ₃ are the same value | 2a |. For example, if a = (a, −a, a, a), then s = (2a, 2a, −2a, 2a). Therefore, from the equations (6), (5), and (9), the peak-to-average power ratio of the DS-CDMA system 100 can be expressed by the following equation.

DS-CDMA System Improvement FIG. 3 shows a DS-CDMA system 300 incorporating the features of the present invention. The example DS-CDMA system 300 provides a spreading factor SF = 8 and reduces the peak-to-average power ratio and bit error probability compared to the conventional DS-CDMA system 100. The DS-CDMA system 300, in various embodiments, compares the (i) rate, (ii) average energy per chip, and (iii) amplitude a of the signal transmitted in the 0th stream with conventional DS-CDMA. It can be the same as system 100. Thereby, the speed of the conventional system can be maintained without increasing the average power per chip. Furthermore, since the power of the signal transmitted in the 0th stream does not change, the bit error probability is the same. Since the 0th stream plays a special role in the system, it is important to keep the bit error probability of the 0th stream as good as the DS-CDMA system 100. For example, when the pilot signal is transmitted using the 0th stream, if the amplitude of the signal decreases, the estimation of the channel fading coefficient becomes inaccurate, leading to failure of decoding of other information streams.

The vector b = (b ₀ , b ₁ , b ₂ , b ₃ , b ₄ , b ₅ , b ₆ , b ₇ ) is obtained from a code book defined later in conjunction with FIG. In the exemplary embodiment, streams 0, 1,. . . , 6 carry information and stream 7 plays an auxiliary role. Variables b ₀ ,. . . , B ₆ sign (polarity) represents the value of the transmitted bit as in the DS-CDMA system 100. For example, a positive entry can correspond to a logic 0 and a negative entry can correspond to a logic 1. Absolute values | b ₀ |,. . . , | B ₇ | represents the amplitude of the transmission signal. In DS-CDMA system 300 of the present invention, with respect to (the desired average as energy E _A is maintained) of different streams of the signal, selecting a different amplitude and polarity.
Spread sequences w ₀ , w ₁ ,. . . , W ₇ can be expressed as follows:
w ₀ = (1,1,1,1,1,1,1,1,)
w ₁ = (1, -1,1, -1,1, -1, -1, -1,)
w ₂ = (1,1, -1, -1, -1,1, -1, -1, -1)
w ₃ = (1, -1, -1, -1,1, -1, -1, -1,1)
w ₄ = (1,1,1,1, −1, −1, −1, −1,)
w ₅ = (1, -1,1, -1, -1, -1, -1,1,)
w ₆ = (1,1, -1, -1, -1, -1, -1,1,1)
w ₇ = (1, -1, -1, -1, -1, -1,1, -1,)

ビットの情報を送信でき、したがって、ＤＳ−ＣＤＭＡシステム３００の速度は、次式のように、従来のＤＳ−ＣＤＭＡシステム１００の速度と同じになる。

７ストリームの情報を送信するためには、２^７のサイズのコード・ブックが必要である。ＤＳ−ＣＤＭＡシステム３００用のコード・ブックを明示的に定義する代わりに、あるアルゴリズムを用いて、そのコード・ブックを定義する。行列Ｇ_ｐｃおよびＧ_ｒｍを次のように定義する。

The sequences w ₀ , w ₁ ,. . . , W ₇ form the rows of an 8-dimensional Hadamard matrix H ₈ so they are orthogonal. Variables b ₁ ,. . . , B ₆ gets a new value every 8 chips, and variable b ₀ gets a new value every m chips. During a time interval of 8 chips, the conventional DS-CDMA system 100 can transmit 6 bits (in 2 cycles). Therefore, in order for the DS-CDMA system 300 to transmit 6 bits in the same 8-chip time interval, six user streams are required. According to one aspect of the invention, the seventh user stream can be used to maintain performance (eg, improve PAPR). Therefore, the DS-CDMA system 300 can be used during m chips.

Bit information can be transmitted, so the speed of the DS-CDMA system 300 is the same as the speed of the conventional DS-CDMA system 100, as follows:

To send information 7 streams, it is necessary code book of 2 ⁷ sizes. Instead of explicitly defining a code book for the DS-CDMA system 300, an algorithm is used to define the code book. The matrices G _pc and G _rm are defined as follows:

The matrices G _pc and G _rm are a single parity check code and a length 8 first-order Reed-Muller code (eg, FJ MacWilliams, NJA Sloane, “The Theory of Error-Collecting Codes”). , North-Holland, 1977). These define the nature of code book B.
Let a be the signal amplitude used in the conventional DS-CDMA system 100, and let c, e, and d be the signal amplitude of the DS-CDMA system 300 of the present invention. 2 ⁷ = 128 binary vectors u = (u ₀ , u ₁ ,..., U ₆ ) from (0, 0,..., 0) to (1, 1,..., 1) Let's take all the possible values of. For each vector u , a corresponding vector b is defined according to the following code book generation process 400 (FIG. 4).
1. v = u G _pc is calculated.
2. Calculate h = G _rm ν ^⊥ (表 す represents vector transpose).
3. If h ^⊥ = (0, 0, 0, 0) and t = 2, otherwise the t = 1.
4). ν _i = 1-2ν _i , i = 0,. . . , 7.
5). The vector b is formed as follows. For t = 1, b ₀ = av ₀ and b _i = cν _i , i = 1,. . . , 7; otherwise, b ₀ = av ₀ , b _i = eν _i , i = 1,. . . , 6 and b ₇ = −dν ₇ .

The vector b forms the code book B.
For example, u = (0, 1, 1, 0, 0, 0, 0). ν = (0,1,1,0,0,1,1,0), and the further h ^⊥ = a (0, 0, 0, 0). Therefore, t = 2 and b = (a, -e, -e, e, ee, -e, d).

It will be apparent that for any vector u where the entries u ₄ , u ₅ , u ₆ are all 0, t = 2. As a further example, let u = (0, 1, 1, 0, 0, 0, 1). ν = (0,1,1,0,0,1,0,1), and the further h ^⊥ = a (0,1,0,0). Therefore, t = 1 and b = (a, -c, -c, c, c, -c, c, -c).
It will be apparent that t = 1 for any vector u in which at least one of the entries u ₄ , u ₅ , u ₆ is not zero.

式（７）のパーセバルの公式を用いると、チップ当たりの平均エネルギーは次式で表される。

PAPR of DS-CDMA system 300
A vector b corresponding to the case of t = 1 is called a first type vector, and a vector b corresponding to the case of t = 2 is called a second type vector. It will be apparent that the number of vectors of the first type is 7.16 = 112 and the number of vectors of the second type is 16.
The power of the first type vector is a ² + 7c ² . The power of the second type vector is a + 6e ² + d ² . The total number of vectors is 2 ⁷ = 128. Therefore, the average energy of the vectors in the code book is given by

Using the Parseval formula of Equation (7), the average energy per chip is expressed by the following equation.

To keep the average energy per chip in the DS-CDMA system 300 the same as in the conventional DS-CDMA system 100, the amplitudes of e, c, and d must be selected such that E _B = E _A. shall _{(E A} is defined by equation (8)).
Consider the PAPR of the DS-CDMA system 300 of the present invention. It will be clear that for an arbitrary vector b of the first kind, the corresponding output vector s = b H ₈ has the same set of absolute values of entries, expressed as:
{| A + 3c |, | a-c |, | a-5c |}
Note that the vector u that generates the first type vector b belongs to the coset of the primary Reed-Muller code with a coset reader weight of 2. The same applies to the second type of vector b . In this case, a set of absolute values of entries of the output vector s = bH is expressed by the following equation.
{| A + 6e-d |, | a + d |, | a-2e-d |}
Therefore, the PAPR of the DS-CDMA system 300 is expressed by the following equation.

In order to obtain a system with a low PAPR, the amplitudes b, c, and e must be chosen to achieve E _B = E _A and minimize Equation (11).
In an exemplary solution to this optimization problem, the following amplitude is obtained:
c = 0.65125123893.a, e = 0.611.a, d = 1.837572876.a
It will be apparent that such a selection results in E _B = E _A and PAPR = 2.014.

であるベクトルが、第１種のベクトルのすべてのペアの中でペア間距離（ｄ_１とする）が最小となることは明らかであろう。同様に、ベクトルの形式が

であるベクトルが、第２種のベクトルのすべてのペアの中でペア間距離（ｄ_２とする）が最小となる。
最後に、ベクトルの形式が

であるベクトルが、一方が第１種のベクトルで他方が第２種のベクトルであるすべてのペアの中でペア間距離（ｄ_３とする）が最小となる。既に示したように、ＳＮＲが高いチャネルでビット・エラー確率を低くするためには、コード・ブックの最小距離を最大化しなければならない。これは、一定振幅ｃ、ｄ、およびｅの値を変更することによって実行できるが、そのようにすると、システムのＰＡＰＲが増える。 Variations of DS-CDMA System 300 Not only is the PAPR small, but it also requires a low bit error probability. In the next section, the decoding algorithm is described. Note that different approaches are used for channels with low signal-to-noise ratio (SNR) and high channels to minimize bit error probability. For channels with a high signal-to-noise ratio, the code book with the larger minimum distance has a lower bit error probability. The minimum distance for code book B is defined by:
d (B) = min {dist ( x , y ) = (x ₀ −y ₀ ) ² + (x ₁ −y ₁ ) ² +. . . + (X ₇ −y ₇ ) ² : x , y ∈ B}
The vector format is

It will be apparent that the vector with the smallest inter-pair distance (d ₁ ) among all pairs of vectors of the first kind. Similarly, the vector format is

Is the smallest pair-to-pair distance (d ₂ ) among all the pairs of the second type vectors.
Finally, the vector format is

Vector is found one the other in the first type of vector (a d ₃₎ Pair distance among all pairs, which is the second type of vector becomes minimum. As already indicated, in order to reduce the bit error probability on a channel with a high SNR, the minimum distance of the code book must be maximized. This can be done by changing the values of constant amplitudes c, d and e, but doing so increases the PAPR of the system.

Let the desired PAPR be 2.2. It will be clear that the minimum of distances d ₂ and d ₃ defines the minimum distance of the code book (distance d ₁ is always much larger than d ₂ and d ₃ ). Therefore, the optimal selection of the constant values c, d, and e is such that d ₂ ≈d ₃ with PAPR _B ≈2.2 and E _A = E _B.

For example, if c = 0.611617844 · a, e = 0.63d ₃ a, and d = 1.813520605d ₃ a, then PAPR≈2.2009 and d ₁ ≈2.992 · a ² , d ₂ = 2 A DS-CDMA system with .987 · a ² and d ₃ = 3.1752 · a ² is obtained.

FIG. 5 shows the relative decoding performance (bit error versus signal-to-noise ratio) of the conventional DS-CDMA system 100 and the inventive DS-CDMA system 300 in the presence of an additive white Gaussian noise (AWGN) channel. Is a plot 500 showing the probability). According to another aspect of the present invention, two different code books are used based on the high and low signal-to-noise ratio (SNR) of the channels distinguished by a predetermined threshold. Therefore, to minimize the bit error probability, different approaches are used for low and high signal-to-noise ratio (SNR) channels. For channels with a high signal-to-noise ratio, the code book with the larger minimum distance has a lower bit error probability. For example, as shown in FIG. 5, when the SNR exceeds 2, the code book associated with the DS-CDMA system 300 of FIG. 3 has a lower bit error probability.
Decoding for DS-CDMA system 300

を送信し、ベクトルｘ＝ｓ＋ｚを受信する。一般性を失うことなく、そのチャネルを付加白色ガウス雑音（ＡＷＧＮ）チャネルとする。すなわち、ベクトルｚの任意の要素の密度関数ｆ（ｚ_ｉ）を次式で表すことができるものとする。

ただし、σはチャネルのＳＮＲに依存する。 For the reconstruction of the variable b ₀ , exactly the same procedure as in the system A is used. In systems B and C, the amplitude of the signal transmitted in the 0th stream is the same as in system A, so the error probability is also the same. The same despreading procedure as in system A can be used for reconstruction information from other streams in systems B and C. However, streams 1, 2,. . . , 7 has a lower signal amplitude than in system A, so the bit error probability is higher. For this reason, in addition to despreading, posterior probability (APP) decoding of the received vector can be performed.
Assume again that the vector b = (b ₀ , b ₁ ,..., B ₇ ) is transmitted. Output vector on noisy channel

And receive the vector x = s + z . Without loss of generality, the channel is an additive white Gaussian noise (AWGN) channel. That is, the density function f (z _i ) of an arbitrary element of the vector z can be expressed by the following equation.

However, σ depends on the SNR of the channel.

３．０から７までのｉについて、以下を実施する。

４．０から７までのｉについて、以下を実施する。

５．終了。 FIG. 6 is a flow chart representing an exemplary decoding process 600. As shown in FIG. 6, the exemplary decoding process 600 performs the following:
For i from 1.0 to 7, calculate y _i = x · w _i .
2. For all b = (b ₀ , b ₁ ,..., B ₇ ) of B, calculate:

For i from 3.0 to 7, do the following:

For i from 4.0 to 7, do the following:

5). End.

Using standard arguments (see, for example, LR Bahl et al., “Optical Decoding of Linear Codes for Minimizing Symbol Error Rate”, IEEE Trans. Inform. Theory, pp. 284-87, 1974). It is clear that the following equation holds:

That, t _i is the log-likelihood ratio of the i-th bit. The algorithm 600 requires about 1000 real number operations.
The embodiments and variations presented herein are merely illustrative of the principles of the present invention and that various modifications can be made by those skilled in the art without departing from the scope and spirit of the invention. I want you to understand.

It is a figure which shows the conventional DS-CDMA system. FIG. 2 shows an exemplary code book that can be used in the DS-CDMA system of FIG. It is a figure which shows the DS-CDMA system incorporating the function of this invention. 6 is a flow chart representing an exemplary implementation of a code book generation process. The relative decoding performance (bit error probability versus signal-to-noise ratio) of the conventional DS-CDMA system of FIG. 1 and the DS-CDMA system of FIG. 3 in the presence of an additive white Gaussian noise (AWGN) channel. It is a plot to show. 3 is a flow chart representing an exemplary implementation of a decoding process.

Claims (10)

A method of generating a code book comprising a plurality of vectors for use in a CDMA system,
Selecting an amplitude value and a polarity value for each vector of the code book to reduce a peak-to-average power ratio.   The method of claim 1, wherein the amplitude value is selected to maintain a desired energy per chip.   The method of claim 2, wherein the desired energy per chip is based on energy per chip of a CDMA system having a lower order diffusion coefficient.   The method of claim 1, wherein the selecting further comprises selecting the amplitude value to reduce a peak-to-average power ratio while maintaining a desired average energy per chip.   Generating a first code book for use under conditions of the first signal to noise ratio; and generating a second code book for use under conditions of the second signal to noise ratio. The method of claim 1. A transmitter in a CDMA system comprising:
A plurality of multipliers, wherein each of the multipliers multiplies the encoded data stream by a corresponding spreading code, and the encoded data stream is based on a code book comprising a plurality of vectors. , Each of the vectors has a non-uniform amplitude value selected to reduce the peak-to-average power ratio;
A transmitter comprising a combiner for combining the outputs of the plurality of multipliers for transmission.   Encoding a data stream based on a code book comprising a plurality of vectors, each of the vectors having a peak-to-average power ratio when the vector includes a constant magnitude coefficient value. A communication method having a coefficient value for reducing an average power ratio.   The method of claim 7, further comprising transmitting the encoded data stream.   The method of claim 7, further comprising the step of multiplying the encoded data stream by a corresponding spreading code. The encoded data stream is in a first code book for use under conditions of a first signal to noise ratio and a second code book for use under conditions of a second signal to noise ratio. The method according to claim 7, which is based on.

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